A vector function is any function whose output is a vector.
Parametric equations are often represented as vector functions in the following manner. This example has a single input () and produces three simultaneous outputs all which are functions of in themselves. The sum of the three components produces the radius vector.
Another example would be a vector function with coordinates as inputs, in the form
This equation represents a two-dimensional vector field.
The derivative of a vector function is equal to
The integral of a vector function is equal to
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